Practice Questions on Engineering Mathematics

 Q1. The function $2x^2-9x-2$ has a minimum value in the interval [2,6]   at:
 A. $\dfrac{7}{4}$. B. $\dfrac{9}{4}$. C. $\dfrac{5}{4}$. D. $\dfrac{3}{4}$.

 Q2. The order of the differential equation, $\dfrac{d^3y}{dx^3}+\left(\dfrac{dy}{dx}\right)^3+x^2+y^4=0$
 A. 4 B. 3 C. 2 D. 1

 Q3. The value of line integral $\int_{c}^{}(3x-y)ds$ and $C$ is the portion of the circle $x^2+y^2=18$ traversed from (-3, 3) counterclockwise around to (3, 3) followed by the line segment from (3, 3) to (1, 2) is:
 A. $54\sqrt{2}+\dfrac{11\sqrt{5}}{2}$ B. $24\sqrt{3}+\dfrac{7\sqrt{5}}{2}$ C. $23\sqrt{2}+\dfrac{9\sqrt{5}}{2}$ D. $54\sqrt{2}+\dfrac{7\sqrt{5}}{2}$

 Q4. Given the shape of helix defined by $x=2\cos t,\;y=t,\;z=2\sin t$ where $0\leq t\leq 6\pi$ and mass density $\rho(x,y,z)=y$
 A. $24\pi^2 \sqrt{6}$ B. $36\pi^2 \sqrt{6}$ C. $24\pi^2 \sqrt{5}$ D. $18\pi^2 \sqrt{5}$

 Q5. If $f(x)=|\cos x|$; then the Fourier series coefficient $a_{0}$ and $b_{0}$ is:
 A. $4/3\pi,\;0$ B. $4/\pi,\;0$ C. $1/3\pi,\;2/3\pi$ D. $5/5\pi,\;4/3\pi$

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